Search results
Results from the WOW.Com Content Network
Digital logic is the application of the Boolean algebra of 0 and 1 to electronic hardware consisting of logic gates connected to form a circuit diagram. Each gate implements a Boolean operation, and is depicted schematically by a shape indicating the operation.
Example Boolean circuit. The ∧ nodes are AND gates, the ∨ nodes are OR gates, and the ¬ nodes are NOT gates. In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits.
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design.
Boolean functions play a basic role in questions of complexity theory as well as the design of processors for digital computers, where they are implemented in electronic circuits using logic gates. The properties of Boolean functions are critical in cryptography , particularly in the design of symmetric key algorithms (see substitution box ).
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs.
In automata theory, combinational logic (also referred to as time-independent logic [1]) is a type of digital logic that is implemented by Boolean circuits, where the output is a pure function of the present input only.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized ...